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Sources & Methodology
Speed of light c = 299,792,458 m/s (exact NIST CODATA). Sound speeds from NIST. EM spectrum bands from ITU Radio Regulations.
NIST CODATA — Speed of Light c = 299,792,458 m/s (exact)
The exact defined value of the speed of light in vacuum, fixed by definition since the 1983 SI redefinition, used for all electromagnetic wavelength-to-frequency conversions in this calculator.
ITU Radio Regulations — Frequency Band Allocations
ITU international frequency allocation table used to identify EM band and application for any calculated frequency and wavelength in this calculator.
Methodology: f = v/λ. Period T = λ/v = 1/f. Angular frequency ω = 2πf (rad/s). Wavenumber k = 2π/λ (rad/m). Photon energy E = hf where h = 6.62607015×10⁻³⁴ J·s. Quick EM approximation: f(MHz) ≈ 300/λ(m) — error 0.07% vs exact value. Speed of sound in air at 20°C = 343 m/s. Speed of light in medium = c/n (n = refractive index).
⏱ Last reviewed: April 2026
How to Convert Wavelength to Frequency
Frequency tells you how many complete wave oscillations occur every second. Wavelength tells you the spatial distance between peaks. For any wave, these two quantities are linked by the wave speed: multiplying them always gives the speed. Rearranging f×λ = v gives f = v/λ.
The Formula
f = v / λ T = λ / v ω = 2πf k = 2π/λ
Green light 550 nm: f = 299792458 / (550×10⁻⁹) = 545 THz • T = 1.84 fs
FM radio 3 m: f = 299792458 / 3 = 99.9 MHz ≈ 100 MHz
Sound 0.780 m in air: f = 343 / 0.780 = 440 Hz (A4 concert pitch)
WiFi 12.5 cm: f = 299792458 / 0.125 = 2.398 GHz ≈ 2.4 GHz
FM radio 3 m: f = 299792458 / 3 = 99.9 MHz ≈ 100 MHz
Sound 0.780 m in air: f = 343 / 0.780 = 440 Hz (A4 concert pitch)
WiFi 12.5 cm: f = 299792458 / 0.125 = 2.398 GHz ≈ 2.4 GHz
Wavelength to Frequency Reference — EM Waves
| Wavelength | Frequency | Band | Application |
|---|---|---|---|
| 300 m | 1 MHz | MF | AM broadcast radio |
| 3 m | 100 MHz | VHF | FM radio |
| 43 cm | 700 MHz | UHF | 4G LTE cellular |
| 12.5 cm | 2.4 GHz | SHF | WiFi 2.4 GHz, Bluetooth |
| 6.0 cm | 5 GHz | SHF | WiFi 5 GHz |
| 10.7 mm | 28 GHz | EHF | 5G mmWave |
| 700 nm | 428 THz | Visible | Red light |
| 550 nm | 545 THz | Visible | Green light |
| 380 nm | 789 THz | Visible | Violet light |
| 0.1 nm | 3.0 EHz | X-ray | Medical imaging |
Wavelength to Frequency — Sound in Air (343 m/s at 20°C)
| Wavelength | Frequency | Application |
|---|---|---|
| 17.15 m | 20 Hz | Bass limit of human hearing |
| 78 cm | 440 Hz | A4 concert pitch |
| 3.43 cm | 10 kHz | Upper treble |
| 1.715 cm | 20 kHz | Upper limit of human hearing |
| 3.43 mm | 100 kHz | Ultrasound (bat echolocation) |
💡 nm to THz shortcut: f(THz) = 299,792.458 / λ(nm). For 1000 nm: 299.8 THz. For 550 nm: 545 THz. For 380 nm: 789 THz. This is used in optical communications where laser wavelengths are specified in both nm (DWDM channel grid) and THz (frequency spacing). For radio: f(MHz) ≈ 300/λ(m) with 0.07% error.
Frequently Asked Questions
f = v/λ. For EM waves in vacuum: f = c/λ = 299792458/λ(m). For 550 nm green light: f = 299792458/(550×10⁻⁹) = 545 THz. For 3 m radio: 99.9 MHz. For sound in air at 0.780 m: f = 343/0.780 = 440 Hz. Frequency and wavelength are inversely proportional at fixed wave speed.
f = c/λ = 299792458/(550×10⁻⁹) = 5.45×10¹⁴ Hz = 545 THz. Period T = 1.84 femtoseconds — one complete oscillation takes about 2 fs. The photon energy is 2.25 eV. This frequency is far too high to measure electronically; it is determined from the wavelength using a diffraction grating and the formula f = c/λ.
f = c/λ = 299792458/3 = 99.9 MHz ≈ 100 MHz. This sits in the VHF FM radio band (87.5–108 MHz). Quick approximation: f(MHz) ≈ 300/λ(m) = 100 MHz. The exact value differs by only 0.07%. A half-wave dipole antenna for 100 MHz is 150/100 = 1.5 m long.
Inversely proportional: f = v/λ. Doubling wavelength halves frequency. For EM waves: 1 m = 300 MHz, 10 cm = 3 GHz, 1 cm = 30 GHz, 1 mm = 300 GHz, 1 µm = 300 THz, 1 nm = 300 PHz. The product f×λ always equals the wave speed c. Knowing this, you can always convert either way.
f = c/λ = 299792458/0.125 = 2.398 GHz ≈ 2.4 GHz. WiFi 5 GHz has λ = 6.0 cm. WiFi 6E 6 GHz: 5.0 cm. 5G 3.5 GHz: 8.57 cm. 5G mmWave 28 GHz: 10.7 mm. Router antennas are sized as quarter-wave: 299792458/(4×2.4e9) = 3.1 cm for 2.4 GHz.
Near-IR 700 nm: 428 THz. 1 µm: 300 THz. Mid-IR 10 µm: 30 THz. Far-IR 100 µm: 3 THz. TV remote 940 nm: 319 THz. CO₂ laser 10.6 µm: 28.3 THz. All computed using f = c/λ. The boundary between far-IR and microwave is at λ = 1 mm (f = 300 GHz).
No. Frequency is constant; only wavelength and speed change. In glass (n=1.5), speed = c/1.5 = 2.0×10⁸ m/s. Green light at 550 nm (545 THz) entering glass keeps its 545 THz frequency but its wavelength shrinks to 550/1.5 = 367 nm inside. When it exits back to air, wavelength restores to 550 nm. Frequency is set by the source; the medium only changes speed and wavelength.
THz = 299792.458 / λ(nm). For 1000 nm: 299.8 THz. For 550 nm: 545 THz. For 380 nm: 789 THz. The constant 299792.458 THz·nm is the speed of light in nm/ps. This conversion is essential in optical fibre DWDM (Dense Wavelength Division Multiplexing) where channels are defined by both nm and THz spacing.
ω = 2πf = 2πc/λ (rad/s). For 550 nm: ω = 2π×545×10¹² = 3.42×10¹⁵ rad/s. Angular frequency is used in wave equations, quantum mechanics, and AC circuit analysis. It relates to wavenumber k via ω = vk. For dispersion-free media, ω/k = v = constant.
T = λ/v = 1/f. For 550 nm light: T = 550×10⁻⁹/299792458 = 1.84×10⁻¹⁵ s = 1.84 femtoseconds. For FM radio 3 m: T = 10.0 nanoseconds. For sound A4 at 0.780 m: T = 2.27 ms. Period is the inverse of frequency — the time for one complete oscillation.
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